Post-Doctoral Research Associate
Mathematical Neuroscience Lab

229 Avery Hall

402-472-7233

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# Math 208: Analytic Geometry and Calculus III

The course grade breaks down as follows:
• 200 points for homework presentations in class (presenting at least 5 times will guarantee full points)
• 100 points for each midterm test
• 200 points for cumulative final exam
If you receive more than x points, you will earn a grade of at least a y, where the pair (x,y) is drawn from (720, A-), (640, B-), (560, C-), (480, D-).

#### Rough Schedule/Homework

Note: homework is listed on the date it is assigned, not the date it is due -- it is always due the following lecture.
 Date Subject Homework 1/8 Functions of two variables (12.1) 12.1:1, 2, 5, 11, 23, 25, 29, 30 1/9 Contours, level curves and isoclines (parts of 12.2-4) 12.2: 11, 13, 14, 17 (use cross sections!); 12.3: 5, 7, 8, 9. 13. 16. 20, 21ab (in your notes, we drew a contour diagram for f(x,y)=x^2+y^2 on Tuesday) 1/11 Linear functions, contours and cross sections for graphing (parts of 12.2-4) 12.2: 1, 2, 15, 17 (for these, draw contours/cross sections!); 12.4: 1-5, 7, 8, 10, 13, 21, 28; Draw cross sections for f(x,y) = (x2 + y2)1/2 and determine what surface it is 1/14 Graphing surfaces and a surface zoo (parts of 12.2, 12.5) 12.2: 4, 5, 8, 10, 16; For each surface on page 671, use the given equation (choosing non-zero values for a,b,c,d) to draw contours and x- and y-cross-sections. Describe these in words, then draw a graph of the surface using your work. 1/15 Functions of 3 variables (12.5) 12.5: 1-3, 8-11, 15, 16-18, 23, 31 1/16 Limits in higher dimensions (12.6) 12.6: 1, 3, 6, 11, 13, 18 1/18 Vectors (13.1, 13.2) 13.1: 1, 5, 7, 12, 15, 28, 29, 31, 40; 13.2: 1-5, 7, 11, 21, 25 1/22 The dot product (13.3) 13.3: 1, 5, 7, 9, 11, 15, 17, 19, 33, 39, 41, 43, 49 1/23 The cross product (13.4) 13.4: 2, 3, 9, 11-13, 19, 21, 27 1/25 First look at partial derivatives (14.1) 14.1: 1, 3, 5, 9-11, 16, 17, 20, 22, 25 (Hint on these: just use what you know about normal derivatives! Also, check the section for alternate notation I didn't get to in class.)For Wednesday's review: construct an outline of everything we have done so far in the class -- be sure to indicate particular techniques and their applications. 1/28 Computing partial derivatives and the tangent plane (14.2-3) 14.2: 1, 3-5, 9, 11, 18, 23, 26, 27, 36, 4314.3: 1, 2, 5, 6, 9, 11, 18, 20, 22, 29 1/29 Directional derivatives and the gradient vector (14.4) 14.4: 1, 4, 5, 7, 15, 17, 22, 24, 27, 29-31, 33 1/30 Exam 1 review -- bring your outlines and questions! 2/1 Exam 1: 12.1-6, 13.1-4, 14.1-4 2/4 The gradient vector in three dimensions (14.5) 14.4:37, 41, 47, 49-50, 53-55, 59, 65, 68-6914.5: 2, 3, 7, 9, 14, 17, 25, 26, 49, 53 2/5 Chain rules (14.6) 14.6:21-21-24, 28, 29 2/6 Chain rule applications (14.6) 14.6: 1, 2, 3, 7, 12, 15-18, 25, 31 2/8 Second partials (14.7) 14.7: 1, 3, 6, 11, 13, 14, 19, 23, 25, 30, 33, 35, 44 2/11 Critical Points (15.1) 15.1: 1-3, 6, 7, 9, 11, 21, 22, 26For problems 3 and 6, plug in nearby points or reason about the function to get the answer. For problems 7, 9, 11 and 26, just find the critical points -- you will classify them tomorrow. 2/12 Classifying Critical Points (15.1) 15.1: 6, 7, 9, 11, 17, 22, 26, 32 2/13 Global Extrema (15.2) 15.2: 2, 7, 18, 20, 23 2/15 Lagrange Multipliers (15.3) 15.3: 1, 11, 13, 18, 19, 22, 43 2/18 Double Integrals (16.1) 16.1: 1,9,11,13,19,26,30 2/19 Iterated Integrals (16.2) 16.2: 1-4, 9, 11, 13, 17, 21, 27, 31, 33, 34, 37, 44 2/20 Triple Integrals (16.3) 16.3: 5, 7, 13, 15, 25, 26, 27, 32, 49, 51, 56, 57 2/22 Integration in Polar Coordinates (16.4) 16.4: 10, 11, 12, 16, 20, 21, 23, 24, 26, 28 2/25 Review for exam 2 2/26 Cylindrical and Spherical Coordinates (16.5) 16.5: 1, 2, 3, 5, 10, 14-16, 25, 26, 28 2/27 Cylindrical and Spherical Coordinates continued (16.5) 16.5: 34, 35, 40, 52, 55, 56, 57, 63 3/1 Exam 2: 14.6-7, 15.1-3, 16.1-4 3/4 Parameterized Curves (17.1) 17.1: 1, 4-7, 9, 19, 21, 22, 26, 28, 29, 35, 49, 70 3/5 Velocity and Acceleration Vectors (17.2) 17.2: 1, 3, 7, 8, 10, 17, 32, 36, 37, 41 3/6 Vector Fields and Flows (17.3-4) 17.3: 1, 2, 4, 5, 7, 9, 13, 15, 16, 20, 26, 27, 3317.4: 1, 5, 8, 9, 17, 18, 20 3/11 Line Integrals (18.1) 18.1: 1-8, 11, 16, 18-21, 24, 26, 33, 36, 42, 46 3/12 Computing Line Integrals (18.2-3) 18.2: 1, 3, 5, 10, 11, 16, 20, 23, 29, 30, 31 3/13 Path independence and the FTC (18.3-4) 18.3: 3, 5, 6, 8, 9, 13, 18-20, 22, 23, 29, 31. 4918.4: 1, 5, 9 3/15 Green's Theorem (18.4) 18.4: 14, 17, 21, 23, 26, 33, 34 3/18-22 Spring Break 3/25 Exam 3 review 3/26 Parameterizing surfaces (17.5) 17.5: 1,5,9-12, 13,17,18,23-25,30,33 3/27 Flux integrals in the simplest case (19.1) 19.1: 1,2,5,6,9,12,13 3/29 Exam 3: 16.5, 17.1-4, 18.1-4 4/1 Computing flux integrals (19.1-19.2) 19.1: 14, 15, 20, 27, 29, 36, 43-4719.2: 1, 3, 5, 6 4/2 Computing flux integrals (cont) (19.2) 19.2: 10,14,16,18,26 4/3 Flux integrals over parameterized surfaces (19.3) 19.3: 1-9 4/5 Computing flux integrals using spherical and cylindrical coordinates (19.2) 19.2: 8,9,15,17,19,21,23 4/8 Divergence (20.1) 20.1: 1,2,6,10,16,19,20,27 4/9 The divergence theorem (20.2) 20.2: 1,2,5,7,14,16,20,29 4/10 The curl of a vector field (20.3) 20.3: 1,2,4,9,11-14 4/12 Stokes' Theorem (20.4) 20.3: 22, 29, 31, 3520.4: 1-3, 8, 10 4/15 Stokes' Theorem (cont) (20.4) 20.4: 2-3, 10, 13,17,23,31 (yes, there are repeats -- there was a dearth of volunteers today!) 4/16 Fundamental theorems (20.5) 4/17 Exam 4 Review 4/19 Exam 4: 17.5, 19.1-19.3, 20.1-20.5 4/22 Review 4/23 Review 4/24 Review 4/26 Review